Simulation of a dendritic microstructure with the lattice Boltzmann and cellular automaton methods

Abstract A new modeling approach combining the lattice Boltzmann method (LB) and the cellular automaton technique (CA) was developed to simulate solidification at the microscale. The LB method was used for the coupled calculation of temperature, solute content and velocity field, while the CA method was used to compute the liquid/solid phase change. To validate the accuracy of the LB–CA model and its efficiency for the simulation of dendrite growth under convection, comparisons of the tip characteristics and dendrite morphologies under various simulation conditions were made with those obtained by analytical means and by a finite element model coupled with the cellular automaton technique (FE–CA model). The results show that the LB–CA model is computationally much more efficient than the FE–CA model for simulations of dendritic microstructures under convection. The tip splitting phenomenon was captured for high cooling rates and with comparatively coarse grids due to mesh-induced anisotropy and thermal instabilities. The simulated dendrite morphologies obtained with various anisotropy and Gibbs–Thomson coefficients were discussed. The results show that the dendrite growth direction does not always follow the crystallographic direction and high branching phenomena can occur with small anisotropy and/or Gibbs–Thomson coefficients.